Question

Over the next four years, the City of Mythica, New York, is expecting the following cash flows from a federal grant: year 1—$150,000; year 2—$220,000; year 3—$250,000; year 4—$175,000. The city wants to use the grant as collateral for a loan, but it is unsure about its net present value. Use Exhibit 26-3 for your solution.

a. What is the net present value of the grant if the rate of return is expected to be 5 percent?
b. What is the net present value of the grant if the rate of return is expected to be 8 percent?

(For all requirements, Round your "PV factor" to 3 decimal places.)

Answer 1

Answer:

a) Determination of Present value of grant received if the rate of return is expected to be 5%:

Present Value

Particulars	Period	PV Factor	Amount	Present Value
Inflow:
Grant received in year-1	1	0.952	$150,000	$142,800
Grant received in year-2	2	0.907	$220,000	$199,540
Grant received in year -3	3	0.864	$250,000	$216,000
Grant received in year-4	4	0.823	$175,000	$144,025
Present Value				$702,365

b) Determination of Present value of grant received if the rate of return is expected to be 8%:

Present Value

Particulars	Period	PV Factor	Amount	Present Value
Inflow:
Grant received in year-1	1	0.926	$150,000	$138,900
Grant received in year-2	2	0.857	$220,000	$188,540
Grant received in year -3	3	0.794	$250,000	$198,500
Grant received in year-4	4	0.735	$175,000	$128,625
Present Value				$654,565